arXiv subjects
Publications and source records attributed to S. Khlebnikov.
Decoherence associated with super-Hubble modes in de Sitter space may have a dual description, in which it is attributed to interaction of sub-Hubble modes with an ``environment'' residing just inside the observer's horizon. We present a version of such description, together with some consistency checks, which it is shown to pass.
We present numerical evidence that a domain wall in a background with varying vacuum energy density acquires velocity in the direction of decreasing Hubble parameter. This should lead to at least a partial relaxation of the cosmological constant on the wall.
We compare decoherence induced in a simple quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We find that even a relatively compact oscillator bath (with the effective number of degrees of freedom of order 10), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case, the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the qubit with the environment.
The final stage of Bose-Einstein condensation in a large volume occurs through coarsening--growth of individual correlated patches. We present analytical arguments and numerical evidence that in the momentum space this growth corresponds to strong turbulence of the particle number, with a turbulent cascade towards the infrared and the power law $n(k) \propto k^{-(d+1)}$ in $d=2,3$ spatial dimensions. As a corollary, we find that the correlation length grows linearly in time, with the speed of order of the speed of Bogoliubov's quasiparticles (phonons). We use these results to estimate the speed of BEC in atomic vapors and in galactic dark matter.
We consider the possibility that tunneling in a degenerate double-well potential in de Sitter spacetime leads to coherent oscillations of quantum probability to find the system in a given well. We concentrate on the case when the mass scale of the potential is much larger than the Hubble parameter and present a procedure for analytical continuation of the ``time''-dependent instantons, which allows us to study the subsequent real-time evolution. We find that the presence of the de Sitter horizon makes tunneling completely incoherent and calculate the decoherence time. We discuss the difference between this case and the case of a $θ$-vacuum, when tunneling in de Sitter spacetime preserves quantum coherence.
We consider decay of the inflaton with a quartic potential coupled to other fields, including gravity, but restricted to spherical symmetry. We describe analytically an early, quasilinear regime, during which inflaton fluctuations and the metric functions are driven by nonlinear effects of the decay products. We present a detailed study of the leading nonlinear effects in this regime. Results of the quasilinear approximation, in its domain of applicability, are found to be consistent with those of fully nonlinear lattice studies. We discuss how these results may be promoted to the full three dimensions.
We numerically integrate the time-dependent Schrodinger equation in a single-degree-of-freedom model of SQUID with a variable potential barrier between the basis flux states. We find that linear superpositions of the basis states, with relatively little residual excitation, can be formed by pulsed modulations of the barrier, provided the pulse duration exceeds the period of small oscillations of the flux. Two pulses applied in sequence exhibit strong interference effects, which we propose to use for an experimental determination of the decoherence time in SQUIDs.
We study numerically evolution of metric perturbations during reheating in a model with two fields and a strong parametric resonance. Our calculation is fully nonlinear and includes gravity but is restricted to spherical symmetry. In this model, super-Hubble metric perturbations can grow during reheating only due to effects nonlinear in fluctuations of the fields. We find that they indeed grow and, soon after the growth begins, dominate variances of the metric functions. Thus, the metric functions become smooth but varying significantly over large scales. Their profiles at late times are interpreted as signalling a gravitational instability and formation of a black hole.
A superconducting ring has different sectors of states corresponding to different values of the trapped magnetic flux; this multitude of states can be used for quantum information storage. If a current supporting a nonzero flux is set up in the ring, fluctuations of electromagnetic field will be able to ``detect'' that current and thus cause a loss of quantum coherence. We estimate the decoherence exponent for a ring of a round type-II wire and find that it contains a macroscopic suppression factor $(δ/ R_{1})^{2}$, where $R_{1}$ is the radius of the wire, and $δ$ is the London penetration depth. We present some encouraging numerical estimates based on this result.
We study numerically evolution of a self-gravitating nonequilibrium Bose gas contained in a fixed volume. We find that, even when the volume is small enough to prevent collisionless instability, a compact phase-correlated object (a Bose star) can form, by gravity alone, from a disordered initial state. We interpret this effect and the associated growth of the density contrast as consequences of a new type of gravitational instability---a nonlinear instability due to stimulated gravitational scattering of the bosons. Our results imply that formation of Bose stars, in regions that have fallen out of the Hubble expansion, may be a quite general phenomenon, not requiring a large preexisting correlation length or any short-range interactions.
We describe macroscopic quantum memory devices based on type-II toroidal superconductors and estimate in one case and compute in another the rates at which quantum information stored in these devices ``degrades'' because of thermal fluctuations. In the case when the entire solid torus is superconducting, the Boltzmann factor in the rate corresponds to a well-defined critical fluctuation, and the rate is suppressed exponentially with the linear size of the system. In the case when superconductivity is confined to the surface of the torus, the rate is determined by diffusive motion of vortices around the torus and does not depend exponentially on the linear size; we find, however, that when the two dimensions of the torus are comparable the rate does not contain the usual volume enhancement factor, i.e. it does not grow with the total surface area of the sample. We describe a possible way to write to and read from this quantum memory.
We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the medium) disturbances and construct lattice models for description of not-so-smooth disturbances, in particular, topological defects; these models are modifications of the diffusive XY model. We find that when the activity on each lattice site is very rigid in maintaining its form, the topological defects - vortices or spirals - nucleate a transition to a disordered, turbulent state.
We consider phase separation in nonequilibrium Bose gas with an attractive interaction between the particles. Using numerical integrations on a lattice, we show that the system evolves into a state that contains drops of Bose-Einstein condensate suspended in uncondensed gas. When the initial gas is sufficiently rarefied, the rate of formation of this quantum dew scales with the initial density as expected for a process governed by two-particle collisions.
This paper has been withdrawn by the author as the conjecture proposed in it is wrong.
We investigate nonthermal phase transitions that may occur after post-inflationary preheating in a simple model of a two-component scalar field with the effective potential $λ(ϕ_i^2 - {\rm v}^2)^2/4$, where $ϕ_1$ is identified with the inflaton field. We use three-dimensional lattice simulations to investigate the full nonlinear dynamics of the model. Fluctuations of the fields generated during and after preheating temporarily make the effective potential convex in the $ϕ_1$ direction. The subsequent nonthermal phase transition with symmetry breaking leads to formation of cosmic strings even for ${\rm v} \gg 10^{16}$ GeV. This mechanism of string formation, in a modulated (by the oscillating field $ϕ_{1}$) phase transition, is different from the usual Kibble mechanism.
During preheating after inflation, parametric resonance rapidly generates very large fluctuations of scalar fields. In models where the inflaton field $ϕ$ oscillates in a double-well potential and interacts with another scalar field $X$, fluctuations of X can keep the ϕto -ϕsymmetry temporarily restored. If the coupling of ϕto X is much stronger than the inflaton self-coupling, the subsequent symmetry breaking is a first-order phase transition. We demonstrate the existence of this nonthermal phase transition with lattice simulations of the full nonlinear dynamics of the interacting fields. In particular, we observe nucleation of an expanding bubble.
Resonant decay of the inflaton produces highly non-equilibrium states dominated by interacting classical waves. We discuss several topics in the theory of formation and evolution of such states.
We study the effect of interlayer tunneling in the gauge theory describing a quasi-two-dimensional paramagnetic metal close to a second-order or weakly first-order antiferromagnetic phase boundary. In that theory, two species of fermions have opposite (rather than equal) charges with respect to the gauge field. We find that single-particle interlayer tunneling is suppressed at low energies. The effect of pair tunneling is analyzed within the $(3-d)$ expansion. The resulting phase diagram has superconducting and non-Fermi-liquid normal phases, and so is compatible with that of the copper-oxide superconductors.